Stat questions

#1
A custom bicycle manufacturer has had to deal with an increased rate of returned bicycles in recent months. Customers are returning bikes because they are not the correct dimensions. The company uses three measurements to calculate the dimensions for their bikes. Inside leg, torso and arm length. They suspect that some customers are incorrectly measuring themselves. The company wants to set up calculations that will tell them when a set of measurements are unrealistic. This will prompt them to double check with the consumer and avoid the problem. Leg u=32.1, Torso u=22.9, Arm u=25.0. They collect data from 20 random sampled customers.



1) Determine if the customer measurements represent typical individuals from the overall population. Create histograms, and look for unusual values. Resolve any issues. Calculate 95% confidence interval for the means. Compare the intervals to the population means. Does your sample data fit the population values?

2) When a customer’s measurements come in, the first test to detect possible problem data is a check of each measurement to see if it is within a reasonable range. What are the high and low (leg, torso and arm) measurements within which 99% of all individuals fall (Note: This is the 99% interval for individuals, not for sample means) Test the three customers below to look for unusual values.

Leg Torso Arm
27 20 19
33 23 26
36 25 27

20 random sampled customers data set:

Leg Torso Arm

32 22 25
35 24 28
30 21 24
33 23 27
31 22 26
30 23 23
29 22 22
37 25 29
35 22 28
28 23 22
33 23 27
30 12 23
32 24 24
27 23 21
34 24 25
29 20 21
33 23 24
34 26 26
34 23 26
28 21 23
26 20 21

:eek: